Besides the introduction of geographical coordinate systems, the epistemological problem of the relation between the concepts of matter and space had an impact on the Newtonian concept of space as a container. This problem has been taken up with a focus on alternative conceptualizations of the relation of space and matter in early modern science and philosophy. Aristotelian physics and the Peripatetic tradition negated the possibility of empty space and instead concentrated on the concept of place. In opposition to this tradition ancient atomism was based on the idea of atoms moving through empty space. In the Renaissance, a transformative development of spatial concepts was triggered by cosmological concerns, namely attempts to replace the Aristotelian world system by alternative systems which were often based on ancient atomistic ideas including the concept of empty space, which implicitly involves the notion of space as a container. The growing corpus of empirical knowledge on mechanics and astronomy eventually stabilized Newton’s concept of a universal space. In Newton’s conception, gravitation is decoupled from the structure of space, which allows for space to be homogeneous and isotropic. Nevertheless this conception was not altogether convincing, so that the debate about space and matter continued. An advanced version of the attempts to distinguish between space and matter resulted from Kant’s criticism which tried to remove metaphysical presuppositions. As a consequence, Kant’s solution to the problem departed from atomism altogether, proposing an early version of matter as an appearance of repulsive and attractive forces.